How do you find the slope of a line passing through f (-4) =1 and f (-1) =-3?

Question

Ethan Adkins · Accepted Answer

See the entire solution process below:

The slope can be found by using the formula: #m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))# Where #m# is the slope and (#color(blue)(x_1, y_1)#) and (#color(red)(x_2, y_2)#) are the two points on the line. Changing the values from the problem's points yields: #m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))# The first and second points in this format are (-4, 1) and (-1, -3), respectively. Changing the values from the problem's points yields: #m = (color(red)(-3) - color(blue)(1))/(color(red)(-1) - color(blue)(-4)) = (color(red)(-3) - color(blue)(1))/(color(red)(-1) + color(blue)(4)) = -4/3#

Julia Adams · Answer

undefined To find the slope of a line passing through two points $ (x_1, y_1) $ and $ (x_2, y_2) $, you can use the formula:

$$ \text{Slope} = \frac{{y_2 - y_1}}{{x_2 - x_1}} $$

Given the points $ (-4, 1) $ and $ (-1, -3) $, let's denote $ (x_1, y_1) = (-4, 1) $ and $ (x_2, y_2) = (-1, -3) $. Then, we can substitute these values into the formula:

$$ \text{Slope} = \frac{{-3 - 1}}{{-1 - (-4)}} $$

$$ \text{Slope} = \frac{{-3 - 1}}{{-1 + 4}} $$

$$ \text{Slope} = \frac{{-4}}{{3}} $$

So, the slope of the line passing through the points $ (-4, 1) $ and $ (-1, -3) $ is $ \frac{{-4}}{{3}} $.